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Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities

Author

Listed:
  • D. T. Peng

    (Beijing Jiaotong University
    Guizhou University)

  • J. Yu

    (Guizhou University)

  • N. H. Xiu

    (Beijing Jiaotong University)

Abstract

This paper is intended mainly to present some generic uniqueness results for a class of vector Ky Fan inequalities. By employing the methods of set-valued analysis, we prove that, in the sense of Baire category, most of the problems in a complete metric space, consisting of vector Ky Fan inequalities satisfying some conditions, have unique solution and that every vector Ky Fan inequality, possessing more than one solution, can be approached arbitrarily by a sequence of vector Ky Fan inequalities each of which has a unique solution. Our discussions are under two different settings. One setting is related to vector Ky Fan inequalities defined on a compact set; the other is related to vector Ky Fan inequalities defined on a noncompact set. The corollaries of our results generalized the corresponding results in the literature.

Suggested Citation

  • D. T. Peng & J. Yu & N. H. Xiu, 2012. "Generic Uniqueness of Solutions for a Class of Vector Ky Fan Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 165-179, October.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:1:d:10.1007_s10957-012-0062-1
    DOI: 10.1007/s10957-012-0062-1
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    References listed on IDEAS

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    1. Alexander J. Zaslavski, 2010. "Optimization on Metric and Normed Spaces," Springer Optimization and Its Applications, Springer, number 978-0-387-88621-3, September.
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    Cited by:

    1. Rabian Wangkeeree & Pakkapon Preechasilp, 2013. "Existence theorems of the hemivariational inequality governed by a multi-valued map perturbed with a nonlinear term in Banach spaces," Journal of Global Optimization, Springer, vol. 57(4), pages 1447-1464, December.

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